We work on fundamental problems in mathematics and theoretical computer science, interact extensively with the academic community and collaborate with other researchers at MSR on challenging applied problems. Among our areas of expertise are probability theory, combinatorics, statistical physics, metric geometry, fractals, algorithms and optimization. We host an amazing array of researchers in these areas: see a full list here.
People
Theory Group - Permanent members
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Interests: Fundamental algorithmic problems such as graph partitioning and network design. Algorithmic challenges in economics and game theory, such as computing market equilibrium and auction design. |
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Interests: Probability theory, with emphasis on discrete spatial models, including cellular automata, percolation, matching, coupling. |
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Interests: Probabilistic Combinatorics, Statistical Physics, Random graphs, Random walks, Mixing times of Markov chains, Extremal Combinatorics. |
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Kostya Makarychev Interests: Approximation algorithms and combinatorial optimization, in particular, semidefinite programming and questions related to functional analysis and metric geometry. |
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Yuval Peres (Manager) Interests: Random walks, Percolation, Mixing times of Markov chains, Brownian motion, Determinantal point processes, Fractals and Hausdorff dimension, Phase transitions, Ergodic theory, Game theory |
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Interests: Approximation Algorithms, Combinatorial Optimization with applications in network design. Also interested in models and problems dealing with uncertainty in data. |
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Interests: statistical physics, dimers, SLE, Markov chain mixing times, randomized algorithms |
Postdocs
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Jason Miller (9/27/2010-6/30/2012) Interests: All forms of probability theory, with a focus on stochastic interface models such as random surfaces and SLE. |
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Shaddin Dughmi (8/15/2011-6/30/2012) Interests: Algorithms, combinatorial optimization, game theory, mechanism design. |
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Alexandre Stauffer (7/5/2011-6/30/2012) Interests: Random walks, percolation, interacting particle systems, mixing time of Markov chains, randomized algorithms. |
Visiting Researchers
- Long-term visitors (see complete list here)
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Béla Bollobás (4/2/2012-5/25/2012) Interests: Extremal graph theory, functional analysis, the theory of random graphs, graph polynomials and percolation. |
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Anna Karlin (1/9/2012-3/2/2012) Interests: Theoretical computer science, design and analysis of algorithms, particularly probabilistic and online algorithms. Also interested in other areas, such as economics and game theory, data mining, operating systems, networks, and distributed systems. |
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David Levin (1/9/2012-3/23/2012) Interests: Probability and Stochastic Processes. In particular, Markov chains, random walks, and related potential theory. |
- Upcoming long-term visitors
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Russell Lyons |
2/7/12 - 10/26/12 |
| Jian Ding | 7/9/12 - 8/31/12 |
| Yossi Azar | 7/16/12 - 8/24/12 |
| László Lovász | 7/30/12 - 8/31/12 |
| Jeff Steif | 8/13/12 - 7/5/13 |
| Tom Bohman | 8/27/12 - 11/16/12 |
- Recent and upcoming visitors
| Pawel Pralat | 5/7/12 - 5/11/12 |
| Lionel Levine | 5/7/12 - 5/16/12 |
| Peter Mörters | 5/7/12 - 5/25/12 |
| Robin Pemantle | 5/14/12 - 5/18/12 |
| Amir Dembo | 6/24/12 - 6/29/12 |
| Van Vu | 6/25/12 - 7/21/12 |
| Richard Kenyon | 7/2/12 - 7/6/12 |
| Fabio Martinelli | 7/2/12 - 7/16/12 |
| Itai Benjamini | 7/2/12 - 7/27/12 |
| Uri Feige | 7/16/12 - 8/10/12 |
| Benny Sudakov | 8/6/12 - 8/17/12 |
| Ben Morris | 8/6/12 - 8/31/12 |
| Niv Buchbinder | 8/6/12 - 8/31/12 |
| Nike Sun | 8/6/12 - 8/31/12 |
In memoriam
- Oded Schramm (died in a tragic accident, September 2008):
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Oded's interests: Percolation, two dimensional random systems, critical systems, SLE, conformal mappings, dynamical random systems, discrete and coarse geometry, mountains |
Topics of Study
The problems on which we are focusing can be broadly classified in three areas: Probability Theory; Combinatorics and Graph Theory; Algorithms and Optimization.
Probability Theory. Here we consider systems with many degrees of freedom, and study dramatic changes in the behavior of these systems as we vary a control parameter. An example which is studied in our group is the phase transition in the random satisfiability problem. Here one studies random logical formulas in conjunctive normal form involving many Boolean variables. As the formulas get longer, there is a phase transition from formulas which are almost always satisfiable to formulas which are almost never satisfiable. Numerical evidence indicates that the hardest instances of the problem are concentrated at the phase transition. We study this phase transition and possible applications of the hardness of the phase transitions to cryptography. Other possible applications of the phase transition work are to image processing (where certain ferromagnetic statistical mechanical models, so-called Potts models, are used to model the colors of different pixels in the image), networks and decision theory.
Combinatorics and Graph Theory. In addition to the more novel efforts of the group, we also do a substantial amount of work on more traditional combinatorics, including graph theory, extremal combinatorics, random graphs, and enumeration. Probabilistic methods play a central role, including advanced probabilistic techniques like high concentration, nibble methods, and Markov chains. Interactions with classical mathematical disciplines like algebra and geometry are explored. These studies provide the theoretical foundations for the application of combinatorial methods in the analysis of algorithms and complexity theory. They also are closely tied with the theory of phase transitions.
Algorithms and Optimization. Algorithms for a variety of problems arising in computing, from data structures to networking, make use of mathematical methods. Our group has expertise in a variety of these methods, including combinatorial optimization, network algorithms and sampling algorithms through rapid mixing. The analysis of algorithms involving probability (either through a random input or an internal random number generation) is a difficult question, which requires the most advanced techniques from discrete probability.
( See recent talks at the Theory Group Seminar )
Applying for Positions
- Applications for a Postdoctoral Researcher position for 2013 received by December 15, 2012 will receive full consideration.
Apply here, and in addition, have your application material (including references) sent to theoryap@microsoft.com. - Apply here for a summer internship and inform us that you have applied by emailing theoryap@microsoft.com.
Additional Links
- Directions to MSR
- Probability in Seattle
- The UW-MSR Theory Center
- Past Members, Postdocs and Interns.
- MSR supported lectures:
- Minicourse on New Random Geometries (2009)
